Teaching unit · Grade 5 (ages 10 to 11)

Decimals: tenths and hundredths

Reading, placing and comparing tenths and hundredths, and linking them to fractions

About four lessons of 45 to 60 minutes

Start here · hook

Decimals are how we write the in-between amounts

A price tag says $2.50, not two dollars and a bit. A sprinter runs the hundred metres in 10.4 seconds, not somewhere around ten. A water bottle holds 0.5 litres. These in-between amounts, the parts smaller than one whole, are written with decimals, and a decimal is just place value carried on past the ones into tenths and hundredths.

Today you will split one whole into ten equal parts and meet the tenth, then split a tenth into ten again and meet the hundredth. You will see that 0.1 and 1/10 are the very same amount written two ways, place a decimal on a number line, and settle the classic playground argument about whether 0.45 is bigger than 0.5.

A price of $2.502 whole dollars, 5 tenths of a dollar (50 cents), 0 hundredths
A time of 10.4 secondsten whole seconds and 4 tenths of a second, and 10.38 is faster than 10.4
A 0.5 litre bottlefive tenths of a litre, the same amount as 1/2 and as 0.50
25 cents is $0.2525 hundredths of a dollar, a quarter of it

Learning objective

What students will be able to do

Students will understand a decimal as place value extended past the ones into tenths and hundredths, read and write tenths and hundredths and link them to fractions such as 1/10 = 0.1, place a decimal on a number line, recognise equivalent decimals such as 0.7 = 0.70, and compare two decimals by reasoning about place value.

Success criteria

I can split a whole into tenths and name one part as 1/10 and as 0.1.
I can read and write tenths and hundredths and say them as fractions.
I can place a decimal between 0 and 1 on a number line.
I can show that 0.7 and 0.70 are the same amount.
I can compare two decimals and explain which is greater.

Curriculum anchor

Standards this unit teaches

5.NBT.A.1Common Core (US)
Place value in decimals
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.3Common Core (US)
Read, write and compare decimals
Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form; compare two decimals to thousandths based on the meanings of the digits in each place, using >, =, and < symbols. This unit works within tenths and hundredths, the first steps toward thousandths.
4.NF.C.6Common Core (US)
Decimal notation for fractions (Grade 4 foundation)
Use decimal notation for fractions with denominators 10 or 100. This Grade 4 standard is where 1/10 is first written as 0.1. The US introduces tenths and hundredths in Grade 4, and Grade 5 deepens it into place-value understanding.
AC9M4N01Australian Curriculum v9 (ACARA)
Decimals to hundredths (Year 4 anchor)
Extend place value to tenths and hundredths and use decimal notation to name and represent these numbers. Australia introduces tenths and hundredths in Year 4, so this unit revisits and deepens the Australian Year 4 concept.
AC9M5N04Australian Curriculum v9 (ACARA)
Add and subtract decimals (Year 5)
Use place value to add and subtract decimals, with estimation and rounding to check that answers are reasonable. The place-value and comparing work in this unit is what this Year 5 descriptor rests on.

Before you start

Prior knowledge

This unit builds on skills students should already have met. Revisit any that are shaky first.

Key vocabulary

Words to teach and display

Decimal: a number with a decimal point, showing parts smaller than one whole
Decimal point: the dot that separates the whole ones from the tenths and hundredths
Tenth: one of ten equal parts of a whole, written 0.1 or 1/10
Hundredth: one of a hundred equal parts of a whole, written 0.01 or 1/100
Place value: the value a digit has because of its position
Equivalent decimals: decimals naming the same amount, such as 0.7 and 0.70

Teaching sequence

Teach it: concrete, pictorial, abstract

The lesson moves from things students can hold, to pictures and diagrams, to the written maths. The diagrams below are drawn from data, so they are accurate and print cleanly. Teach straight from them.

1. A new place to the right of the ones: tenths

Concrete

Take one whole, a strip or a square, and split it into ten equal parts. Each part is one tenth. You already know how to write that as a fraction, 1/10. The decimal way is to add a new place to the right of the ones, marked off by a decimal point, and write one tenth as 0.1. They are the same amount, one of ten equal parts of the whole, written two ways.

The pattern of place value carries straight on. Going left, each place is ten times bigger. Going right past the ones, each place is ten times smaller: the tenths place is a tenth of the ones. So 0.1 is a tenth of 1, exactly as 1 is a tenth of 10.

Count the tenths along a number line from 0 to 1 and they name themselves: 0.1, 0.2, 0.3 and so on up to 1.0, which is ten tenths, one whole again.

One whole split into 10 equal parts. One part shaded is 1/10, written 0.1 as a decimal.

The whole from 0 to 1 split into ten equal tenths. Each tick is one tenth more than the last.

Check for understanding, ask

How many tenths are in one whole?
Write one tenth as a fraction and as a decimal.
Is the tenths place ten times bigger or ten times smaller than the ones place?

2. Reading and writing tenths

Pictorial

Read a decimal by its place value, not just its digits. 0.7 is not point seven with no meaning, it is seven tenths, and seven tenths is 7/10. Show the same amount three ways every time: the shaded bar, the fraction 7/10, and the decimal 0.7. Saying the place value aloud is what makes the decimal a number rather than a pair of symbols.

Placing a decimal follows the fraction exactly. To place 0.7, split 0 to 1 into ten equal tenths and count seven jumps from 0. It lands seven tenths of the way to 1, the same point 7/10 would.

Worked example

Write 0.7 as a fraction and place it on a number line from 0 to 1.

0.7 is seven tenths, so as a fraction it is 7/10.
Split 0 to 1 into ten equal tenths.
Count seven tenths from 0 and mark the point.

0.7 is seven equal tenths from 0, the same point as the fraction 7/10.

Answer: 0.7 = 7/10, and it sits at the seventh tenth, seven tenths of the way from 0 to 1.

Check for understanding, ask

Say 0.3 in words as a fraction.
Where does 0.9 sit compared with 1? How far apart are they?

3. Hundredths: split each tenth into ten

Pictorial

Split one of those tenths into ten equal parts and each new part is one hundredth, written 0.01, the same as 1/100. There are a hundred of them in one whole. Money is the everyday model: a dollar split into a hundred cents means each cent is one hundredth of a dollar, so 25 cents is 0.25 of a dollar, which is 25/100.

Because ten hundredths make one tenth, you can write any tenth as hundredths: 0.7 is the same as 0.70, seven tenths is seventy hundredths. Writing a zero in the hundredths place does not change the value, it just describes the same amount more finely. This is the key to comparing decimals in the next section.

And 0.25 is a familiar amount in disguise: 25 hundredths is 25/100, which simplifies to a quarter. A quarter of a dollar is a quarter, twenty-five cents, 0.25. Fractions and decimals are two languages for the same numbers.

Seven tenths shaded, 0.7. Split each tenth into ten and the same shading is 70 hundredths, so 0.7 = 0.70.

Worked example

Write 25 cents as a decimal part of a dollar and as a fraction.

A dollar is one whole, split into 100 cents, so each cent is one hundredth, 0.01.
25 cents is 25 hundredths, written 0.25.
As a fraction that is 25/100, which is the same amount as 1/4.

Answer: 25 cents is $0.25, which is 25/100, the same as a quarter.

Check for understanding, ask

How many hundredths are in one tenth?
Write 0.5 as hundredths. Does adding the zero change the amount?

4. Comparing decimals

Abstract

The famous trap: is 0.45 bigger than 0.5, because 45 is bigger than 5? No. Compare decimals by place value, largest place first, exactly as with whole numbers. The safe method is to line up the decimal points and pad the shorter one with a zero so both have the same number of places, then compare. 0.5 becomes 0.50, and now 0.50 against 0.45 is fifty hundredths against forty-five hundredths, so 0.5 is greater.

The runner's stopwatch makes it real, with a twist: for a time, smaller is faster. A runner who clocks 10.38 seconds beats one who clocks 10.4 seconds, because 10.38 is less than 10.40. Line up the points and compare: the tenths are 3 against 4, so 10.38 is the smaller time and the faster run.

On the number line 0.45 sits just before 0.5, so 0.5 is the greater number even though 45 looks bigger than 5.

Worked example

Which is greater, 0.5 or 0.45? Then, which runner is faster, 10.4 s or 10.38 s?

Pad to the same places: 0.5 becomes 0.50. Compare 0.50 and 0.45: fifty hundredths beats forty-five hundredths, so 0.5 is greater.
For the times, pad 10.4 to 10.40 and compare with 10.38. In the tenths place, 3 is less than 4, so 10.38 is the smaller time.
Smaller time means faster, so 10.38 s is the faster run.

Answer: 0.5 > 0.45, and 10.38 s is faster than 10.4 s.

Check for understanding, ask

Fill in > or <: 0.6 __ 0.06.
Why does padding 0.5 to 0.50 make the comparison with 0.45 clear?

Watch for

Common misconceptions and how to address them

Misconception0.45 is bigger than 0.5 because 45 is bigger than 5.

Why it happens: Students read the digits after the point as a whole number and forget place value, the classic longer-is-larger error.

How to address it: Pad to the same number of places: 0.5 is 0.50, so it is fifty hundredths against forty-five hundredths. Show it on the number line, where 0.45 sits just short of 0.5.

0.45 lands just before the halfway point 0.5, so 0.5 is the greater number.

Misconception0.1 and 1/10 are different kinds of number.

Why it happens: Decimals and fractions are taught as separate topics, so students do not see them as the same amount.

How to address it: Shade one part of a ten-part bar and label it both ways at once: 1/10 and 0.1. They mark the same shaded amount and the same point on a number line.

One shaded part of ten is 1/10, and 1/10 is exactly 0.1. Same amount, two notations.

MisconceptionThe tenths digit is just the first number after the point, with no particular value.

Why it happens: Students learn to say point seven without ever naming it as seven tenths, so place value never lands.

How to address it: Always read the place: 0.7 is seven tenths, 0.07 is seven hundredths. Put the digit in a place-value chart to the right of the ones and name its place out loud.

Misconception0.7 and 0.70 are different, because 0.70 has an extra digit.

Why it happens: An extra zero looks like more, echoing the longer-is-larger habit.

How to address it: Seven tenths equals seventy hundredths, so the extra zero only describes the same amount more finely. Shade seven tenths, then split each tenth into ten and count seventy hundredths, the shading does not move.

Seven tenths shaded is the same shaded length as seventy hundredths, so 0.7 = 0.70.

MisconceptionTo compare decimals, line them up by the last digit, like whole numbers.

Why it happens: Students right-align numbers out of habit, which misaligns the places once a decimal point is involved.

How to address it: Line up the decimal points, not the last digits, so tenths sit under tenths and hundredths under hundredths. Then pad with a zero and compare place by place.

MisconceptionMultiplying always makes a number bigger, so a decimal answer cannot be smaller than what you started with.

Why it happens: Every whole-number product they have met so far grew, so the rule feels universal.

How to address it: This is a preview, not the focus of the unit, but flag it: half of 8 is 4, and 0.5 times 8 is also 4, smaller than 8. Multiplying by an amount less than 1 gives less. It heads off a Grade 5 stumbling block.

Do it together

Guided practice (with answers)

1. Write 3/10 as a decimal.
Answer: 0.3, three tenths.
2. Write 0.9 as a fraction.
Answer: 9/10, nine tenths.
3. Place 0.4 on a number line from 0 to 1.
Answer: Split 0 to 1 into ten tenths and count four from 0. It lands at four tenths.
4. Which is more, 0.6 or 0.06?
Answer: 0.6, six tenths, which is much more than six hundredths.
5. Write 0.25 as hundredths and as a fraction.
Answer: 25 hundredths, 25/100, the same amount as a quarter.
6. Two runners clock 12.5 s and 12.45 s. Who is faster?
Answer: 12.45 s. Pad 12.5 to 12.50, and 12.45 is less than 12.50, and a smaller time is faster.

On their own

Independent practice worksheets

Set the matching ChalkBee worksheets for independent work. The answer keys are computed in code, so they are never wrong. Start with reading and writing tenths and hundredths, then move to comparing.

Grade 5 decimals worksheet (Set A)read, write and place tenths and hundredths Grade 5 decimals worksheet (Set B)more decimal practice Grade 4 decimals worksheet (foundation)tenths and hundredths first steps for students who need them All decimal worksheetsthe full set across grades All fraction worksheetsthe fraction side of the same numbers

Reach every student

Differentiation

Support

Keep the ten-part bar and a hundred-square in front of students so every decimal has a picture.
Use money throughout: cents are hundredths of a dollar, a model most students already trust.
Limit to tenths until reading and placing are secure, then introduce hundredths.
For comparing, always pad to the same number of places before deciding.

Extension

Introduce thousandths and read 0.125 as one hundred twenty-five thousandths, bridging to 5.NBT.A.3 in full.
Order a set of five decimals with mixed tenths and hundredths from least to greatest.
Write a decimal three ways: as a fraction, a decimal and an amount of money.
Ask which is bigger, 0.5 or 3/10, forcing a fraction and a decimal into the same comparison.

Check it stuck

Assessment: exit ticket

A three-question exit ticket in the last five minutes. It samples the fraction link, equivalent decimals, and comparing.

1. Write 0.7 as a fraction.
Answer: 7/10, seven tenths.
2. Fill in >, < or =: 0.3 __ 0.30.
Answer: 0.3 = 0.30. Three tenths is the same as thirty hundredths.
3. Which is greater, 0.8 or 0.75?
Answer: 0.8. Padded to 0.80, it beats 0.75, eighty hundredths against seventy-five.

For the teacher

Teacher notes and timings

Rough timing across four lessons: Lesson 1 tenths and the fraction link (section 1), Lesson 2 reading and placing tenths (section 2), Lesson 3 hundredths and money (section 3), Lesson 4 comparing plus the exit ticket (section 4 and assessment).
Language to keep saying: seven tenths not point seven, the same amount two ways, line up the point and pad with a zero. These phrases pre-empt most of the misconceptions.
The number lines label only the tenths students need, to keep them readable. Since this is the decimals unit, showing decimal labels is the point, unlike a younger grade where the labels would be hidden.
Money is the strongest model here because students already know a dollar has a hundred cents. Reach for it whenever hundredths feel abstract.
Curriculum note and a US and AU divergence: both systems introduce tenths and hundredths before Grade 5, the US in Grade 4 (4.NF.C.6) and Australia in Year 4 (AC9M4N01). US Grade 5 (5.NBT.A.1, 5.NBT.A.3) deepens this into place-value understanding and extends to thousandths, and the Australian Year 5 code that relies on it is AC9M5N04. So treat this unit as the consolidation year, not the first exposure.
Present mode and print both work: use the Print button for a clean teacher copy or a student handout, and project the page to teach straight from the diagrams.

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